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Osher, Stanley; Sethian, James A.

Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. (English) Zbl 0659.65132

J. Comput. Phys. 79, No. 1, 12-49 (1988).
New methodologies are formulated for following fronts propagating with curvature-dependent speed, which models, among other things, crystal growth and flame propagation. The algoritms are based on an approximation of the Hamilton-Jacobi formulations for such problems. The paper is carefully written with numerical exemplification (including detailed graphics) which shows that the numerical schemes accurately capture the formation of sharp gradients and cusps in the moving fronts.
Reviewer: R.S.Anderssen

Cited in 34 Reviews
Cited in 2142 Documents

MSC:

65Z05 Applications to the sciences
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35L65 Hyperbolic conservation laws
80A25 Combustion
82D25 Statistical mechanics of crystals

Keywords:

hyperbolic conservation laws; numerical example; following fronts propagating; curvature-dependent speed; crystal growth; flame propagation; Hamilton-Jacobi formulations; moving fronts
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\textit{S. Osher} and \textit{J. A. Sethian}, J. Comput. Phys. 79, No. 1, 12--49 (1988; Zbl 0659.65132)
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References:

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